This is the 10206th most frequent Russian word.
благодарно
Gratefully.
The adverb 'благодарно' is used to describe the manner in which she smiled, indicating gratitude.
Она улыбнулась благодарно.
She smiled gratefully.
Here, 'благодарно' modifies 'посмотрел,' describing the grateful feeling expressed through his look.
Он посмотрел на меня благодарно, когда я помог ему.
He looked gratefully at me when I helped him.
In this case, 'благодарно' is used to convey the sense of gratitude accompanying the acceptance of the gift.